Spoken word tends to be um………like that, you know.
I spent some time as a student earning a couple of quid on the side typing out transcriptions of recorded meetings. I had to include everything.
I think most of us would find our own non-scripted verbal utterances highly embarrassing. It's undoubtedly a skill one can improve on, but the conflict between producing genuinely reflective responses to live questions in an eloquent manner is right at the limit of what the human brain can do, given the infinite number of ways of phrasing a response that actually answers the questions, and the nature of the linear structure of language.
Off the top of my head, I can't think of anyone at all who has really captured my attention like that: Obama was pretty good, I think, but I suspect he relied on chunks and formulas he'd used before.
That said - listen to this, and it seems he has few "ums" and "you knows", just the odd "and and and". Other than that, he takes his time. That said, he's already got clear ideas in his head, which he can order in an effective fashion, and has a good enough brain to produce a pretty eloquent argument to an impromptu question. An transcription would need little tidying up to make a decent written piece.